文章基本信息

标题：A dynamically consistent nonstandard finite difference scheme for a predator–prey model
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作者：Muhammad Sajjad Shabbir ; Qamar Din ; Muhammad Safeer 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2019
卷号：2019
期号：1
页码：1-17
DOI：10.1186/s13662-019-2319-6
出版社：Hindawi Publishing Corporation
摘要：The interaction between prey and predator is one of the most fundamental processes in ecology. Discrete-time models are frequently used for describing the dynamics of predator and prey interaction with non-overlapping generations, such that a new generation replaces the old at regular time intervals. Keeping in view the dynamical consistency for continuous models, a nonstandard finite difference scheme is proposed for a class of predator–prey systems with Holling type-III functional response. Positivity, boundedness, and persistence of solutions are investigated. Analysis of existence of equilibria and their stability is carried out. It is proved that a continuous system undergoes a Hopf bifurcation at its interior equilibrium, whereas the discrete-time version undergoes a Neimark–Sacker bifurcation at its interior fixed point. A numerical simulation is provided to strengthen our theoretical discussion.
关键词：39A30;40A05;92D25;92C50;Predator;prey model;Nonstandard finite difference scheme;Persistence;Stability;Neimark;Sacker bifurcation